Mourinho leapt from his seat on United's bench to confront Marco Ianni after Sarri's assistant coach celebrated Ross Barkley's dramatic late equaliser for Chelsea by pumping his fists in front of the away dugout at Stamford Bridge.
Substitute Ross Barkley struck with virtually the last kick of the game in the 96th minute to salvage the hosts' unbeaten start under Maurizio Sarri and spark a touchline melee as Mourinho took offence at the excessive celebrations of one of Sarri's backroom staff.
Mourinho, who lived up to his promise not to celebrate unduly if United scored, said: "No, I don't think I got that respect back but that's not my responsibility".
Users immediately drew parallels to a recent episode of Khabib Nurmagomedov attacking his sparring partner Conor McGregor after a UFC 229 fight.
Mourinho has been charged by the English Football Association for abusive language after a 3-2 win over Newcastle United this month, a match which Manchester United had been losing, adding to speculation that his job was on the line. I think we deserve much more than this result but this is what it is. They have both apologised to me, I accept. "What I did here today I will do in Madrid, in Milan, in Porto, the reaction from the fans is not up to me", Mourinho told reporters. I spoke with my staff, and then [Ianni] agreed to speak to Mourinho and say sorry.
Having trailed to Antonio Rudiger's 21st-minute header, when Paul Pogba's slack marking allowed the German defender to score from a set piece, United produced a stirring second-half performance to come within a whisker of winning at Stamford Bridge for the first time since 2012. Everything is going well for them, they have good results. And individually in the second half, they raised the bar.
Sarri was furious at dropping two points, accusing his players of trying to match United at their own game.
Maybe player-by-player, they are the best team in the league.
When Sky Sports asked Mourinho about what happened, he said had told Ianni to "forget it".